The West African nation has been governed for more than two months by a military regime which took power after deposing Niger's elected president Mohamed Bazoum.
"The Algerian government has received via the Nigerien ministry of foreign affairs a [statement of] acceptance of Algerian mediation aimed at promoting a political solution to the crisis in Niger," the Algerian Foreign Ministry said.
Algerian President Abdelmadjid Tebboune has said Foreign Minister Ahmed Attaf will be "visiting Niamey as soon as possible with the aim of launching discussions ... with all stakeholders", the statement said.
There was no immediate comment from Niger's ruling junta, which has said it wants a three-year transition process.
The Ecowas bloc of West African nations has tried to restore political order in Niger through diplomacy but said it was ready to deploy a regional military force if its efforts were unsuccessful.
Algeria has repeatedly warned against any military response to the crisis in neighbouring Niger. In late August, Mr Attaf said Algiers was proposing a transition period of up to six months to "formulate political arrangements with the acceptance of all parties in Niger without excluding any party".
In its statement on Monday, Algiers said "the acceptance of the Algerian initiative strengthens the prospect of a political solution to this crisis".
The mediation would "pave the way" towards a "peaceful" resolution of the crisis, it added, saying such an outcome is in the interest "of the entire region".